Question

Medians BE and CF of a triangle ABC are equal. Prove that the triangle is an isosceles.
Hint. ( Point of intersection of medians divides them in the ratio 2:1)​

Answer 1

Lets take the triangle BCF and triangle EBC

FC = EB

Angle ECB = Angle FBC

BC is the common side

So triangle ECB and triangle FBC are congruent

FB = EC

And AF = AE

SO FB +AF = EC+ AE

AB = AC ( PROVED)

Answer 2

Explanation:

lets take the traiangle BCF and traingle EBC

FC=ED

angle ECB= angle FBC

BC is the common side

so traingle ECB and traingle FBC are congruent

FB=EC

and AF=AE

so FB+AF=EC+AE

AB=AC (proved)